I haven't posted anything yet so I'll start with a question from chapter 1 I just rediscovered.
On page 5 in Chapter 1, Horkheimer references Platonism's integration of the Pythagorean theory of numbers into a method of objective reasoning. My question is when and how did mathematics transition from a instrument of objective reasoning to subjective reasoning?
Or is the history of the Pythagorean theory as it relates to Philosophy different from how we learn about it in Geometry?
--Annie
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This is really a question about the philosophy of mathematics. Good overview here:
ReplyDeletehttp://plato.stanford.edu/entries/philosophy-mathematics/
Intuitionism holds that "mathematics is essentially an activity of construction. The natural numbers are mental constructions, the real numbers are mental constructions, proofs and theorems are mental constructions, mathematical meaning is a mental construction, … . Mathematical constructions are produced by the ideal mathematician, i.e., abstracted from contingent, physical limitations of the real-life mathematician. But even the ideal mathematician remains a finite being. She can never complete an infinite construction, even though she can complete arbitrarily large finite initial parts of it."
Intuitionism would be consistent with subjective reason, while Platonism within the philosophy of mathematics held sway until sometime in the 19th c.